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New Advances on Chaotic Intermittency and its Applications

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Feldname	Details
Vorliegende Sprache	eng
ISBN	978-3-319-47836-4
Name	Elaskar, Sergio
Name	del Río, Ezequiel
Name ANZEIGE DER KETTE	del Río, Ezequiel
T I T E L	New Advances on Chaotic Intermittency and its Applications
Verlagsort	Cham
Verlag	Springer
Erscheinungsjahr	2017
Erscheinungsjahr	2017
Umfang	Online-Ressource (XVIII, 197 p. 99 illus., 62 illus. in color, online resource)
Reihe	SpringerLink. Bücher
Titelhinweis	Druckausg.ISBN: 978-3-319-47836-4
Titelhinweis	Printed editionISBN: 978-3-319-47836-4
ISBN	ISBN 978-3-319-47837-1
Klassifikation	TGMD
	TEC009070
	SCI041000
	*37-02
	37D45
	37N35
	93D99
	60H30
	34H10
	620.1
	TA349-359
Kurzbeschreibung	One of the most important routes to chaos is the chaotic intermittency. However, there are many cases that do not agree with the classical theoretical predictions. In this book, an extended theory for intermittency in one-dimensional maps is presented. A new general methodology to evaluate the reinjection probability density function (RPD) is developed in Chapters 5 to 8. The key of this formulation is the introduction of a new function, called M(x), which is used to calculate the RPD function. The function M(x) depends on two integrals. This characteristic reduces the influence on the statistical fluctuations in the data series. Also, the function M(x) is easy to evaluate from the data series, even for a small number of numerical or experimental data. As a result, a more general form for the RPD is found; where the classical theory based on uniform reinjection is recovered as a particular case. The characteristic exponent traditionally used to characterize the intermittency type, is now a function depending on the whole map, not just on the local map. Also, a new analytical approach to obtain the RPD from the mathematical expression of the map is presented. In this way all cases of non standard intermittencies are included in the same frame work. This methodology is extended to evaluate the noisy reinjection probability density function (NRPD), the noisy probability of the laminar length and the noisy characteristic relation. This is an important difference with respect to the classical approach based on the Fokker-Plank equation or Renormalization Group theory, where the noise effect was usually considered just on the local Poincaré map. Finally, in Chapter 9, a new scheme to evaluate the RPD function using the Perron-Frobenius operator is developed. Along the book examples of applications are described, which have shown very good agreement with numerical computations
2. Kurzbeschreibung	Chapter 1: Introduction to chaotic intermittency -- Chapter 2: Other types of intermittency and some recent advances in the study of chaotic intermittency -- Chapter 3: Some applications of the chaotic Intermittency -- Chapter 4: Classical theory about noise effects in chaotic intermittency -- Chapter 5: New formulation of the chaotic intermittency -- Chapter 6: New formulation of the noise effects in chaotic intermittency -- Chapter 7: Application of the new formulation to pathological cases -- Chapter 8: Application to dynamical systems. An example with discontinuous RPD: the derivative nonlinear Schrodinger equation -- Chapter 9: Evaluation of the intermittency statistical properties using the Perron-Frobenius operator
SWB-Titel-Idn	482172622
Signatur	Springer E-Book
Bemerkungen	Elektronischer Volltext - Campuslizenz
Elektronische Adresse	$uhttp://dx.doi.org/10.1007/978-3-319-47837-1
Internetseite / Link	Volltext
Siehe auch	Cover
Siehe auch	Inhaltstext

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